It means 'extremely'.

If you say 'House prices in central London are mind-bogglingly high' it means that they are amazingly high, incredibly high...so high that that you can hardly believe it.

mind-bogglingly is the adverb form

I think you mean "mind boggling." It simply means something that is very hard to believe or sensational.

Something that boggles the mind is mind boggling and if something is mind bogglingly (fill in the blank) it means what Su Ki said, that it blows your mind, surprises you a lot or you just can't believe it. 

Definition of to boggle from merriam webster dictionary:

to be unable to think clearly : to be amazed or overwhelmed

: to make (the mind) unable to think clearly : to amaze or overwhelm (the mind)